Certain Aspects of the Theory of Equations for a Pair of Matrices |
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Contents
Introduction | 2 |
A BBA³ 0 | 6 |
Properties P and P₂ for Second Order Matrices | 25 |
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Common terms and phrases
a₂ associated assume B₁ b₁₂ b₂ block c₁ c₂ canonical form characteristic equation chosen columns consider consistent Corallary corresponding d₂ denote determined distinct characteristic values element elementary divisors equa equal equation of F example factor fixed form of type function Given gives Hence k₁ K₁₂ k₂ least left invariant direction Lemma minimum equation namely necessary and sufficient non-singular second order notation occur P₂ paired problem Progression proof property P3 prove R₁ rank repeated respectively restrictions resultant right invariant direction roots rows S₂ satisfies scalar second equation second order matrices Similarly ß₁ ß₂ Substituting sufficient condition suppose term Theorem Third Order Matrices tion transform values of F vanish write X₁ zero α₁ α₂ αι